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Vietnam
Journal of Mathematics 37:4 (2009) 515-525
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On Generalized δ-Supplemented Modules
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Yahya Talebi and
Behnam Talaee
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Abstract. Let M be a module and N,
K submodules of M. N is called a generalized supplement of K
in M if, M= N + K and N ∩ K
≤ Rad(N). A module M is called a generalized
supplemented module (briefly a GS-module) if any submodule of M has
a generalized supplement in M. Also M is called a generalized
amply supplemented (briefly a GAS-module) if whenever M = A +
B for submodules A, B of M, then A has a
generalized supplement in M contained in B. It is clear that
any supplemented module (amply supplemented module) is a GS-module
(GAS-module). In this paper we investigate generalizations of these
modules. We will show that a module M is Artinian if and only if M
is a δ-GAS-module and satisfies DCC on generalized δ-supplment
and δ-small submodules.
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2000 Mathematics Subject Classification: 16D10, 16D90,
16P70.
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Keywords: GS-module, GAS-module, δ-GS-module,
δ-GAS-module.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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